Question 697815
The runner and the walker will meet again at their original starting point after 1 hour.
At that time the runner will have completed 7 turns and the walker would have completed 2 turns.
The walker completes one turn and is passing by the starting point after 0.5 hour, but at that time the runner has gone 3.5 turns and is on the opposite side of the track.
The first time they pass each other, the walker has gone a short distance around the track, while the runner has covered the rest of the distance around the track.
Between the two of them they have covered the whole track 1 time (1 km total distance).
The second time they pass each other, they have covered the whole track twice (2 km total distance).
The nth time they pass each other, between the two of them, they have covered {{{n}}} turns (a distance of {{{n}}} km).
In {{{t}}} hours, the runner covers {{{7t}}} km.
In {{{t}}} hours, the walker covers {{{2t}}} km.
In {{{t}}} hours, between the two of them, they cover
{{{7t+2t=9t}}} km.
When they meet for the nth time,
{{{9t=n}}}
At {{{t=1}}} hour, {{{9*1=n}}} --> {{{n=9}}} they are meeting for the 9th time at their starting point.
Before that, they had met {{{highlight(8)}}} times, at different points around the track.